pub fn new_birthday_probability(n: u32) -> f64 {
    if n > 365 {
        return 1.0; 
    }
    let mut probability_no_shared = 1.0;

  
    for i in 0..n {
        probability_no_shared *= (365 - i) as f64 / 365.0;
    }

    1.0 - probability_no_shared
}